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 A293624 Fermat pseudoprimes to base 2 that are square pyramidal numbers. 7

%I

%S 24301222105,34200607741,194305088689,7362505969365,19702357790989,

%T 2985533798982149,6091629437910701,24781034010920641,

%U 98129837465651129,99860491537987361,105697961209955269,154533752639483489,406611602100644641,714567498159333701

%N Fermat pseudoprimes to base 2 that are square pyramidal numbers.

%C Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.

%C Intersection of A001567 and A000330.

%C The corresponding indices of A000330 are 4177, 4681, 8353, 28057, 38953, 207673, 263401, 420481, 665233, 669121, 681913, 773953, ...

%H Andrzej Rotkiewicz, <a href="http://gdz.sub.uni-goettingen.de/dms/load/mod/?PPN=PPN378850199_0028&amp;DMDID=DMDLOG_0007">On pyramidal numbers of order 4</a>, Elemente der Mathematik, Vol. 28 (1973), pp. 14-16.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H">Schinzel's Hypothesis H</a>.

%t p[n_]:=n(n+1)(2n+1)/6; Select[p[Range[3, 10^6]],PowerMod[2,(#-1),#] == 1 &]

%Y Cf. A000330, A001567, A293625.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 13 2017

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Last modified May 23 13:25 EDT 2019. Contains 323514 sequences. (Running on oeis4.)